Peer-to-Peer (P2P) networks are one way to create large-scale distributed systems. A single peer has only a limited view on other peers. Thus, efficient searching for other peers or their content is a key performance indicator. In this paper, we investigate the search efficiency in an m-ary tree-structured P2P overlay. While previous work aimed for balancing the maximum height of a node's sub-trees, we show that keeping the height balanced throughout the overall network -a property called null-balance -will increase search performance considerably. Simulations using the ns-3 discrete-event simulator show 50% better performance w.r.t. required routing hops in these nullbalanced trees. Therefore, we develop algorithms that keep a tree null-balanced if a node joins or departures. I.e., we prevent the need for restructuring. As we show, the cost of our efficient structure-preserving algorithms is easily set off by a relatively small number of search operations.